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# Reducing the number of degrees of freedom

I have been reading the book by Prof Anil K Chopra on Structural Dynamics. You might all be aware that Prof Chopra is from University of California Berkeley.

I have been reading the chapter 14, wherein the author talk of reducing the dynamic degrees of freedom using Rayleigh Ritz method.My question is, in commercial FE software , is the reduction of dynamic degrees of freedom practised?

If yes, what are the methods used? IS Rayl;eigh Ritz approiach used?

Kajal

Forums:

## yes and no

First, R-R method in Ch. 14 of Chopra is not the original version which was for continuous systems, though the philosophy behind is the same.

Second, FE is based on approximation of the solution with local/compact support, while R-R approximates the solution with admissible shape function with global value.

Finally, R-R is used in FE codes by further assumption that Ritz shape function is approximated by FE expansion, as the combination of original R-R and basic FE methodology.

## Guyan reduction

Does Guyan reduction also hold the same philospopgy as Rayleigh Ritz- when I say philosophy, I mean its primary aim being to reduce the number of degrees of freedom??

## Guyan reduction and R-R

Hi,

When Guyan reduction is used for reducing the DoF (or selecting Master DoF (MDoF)), there are certain guidelines for selection of MDoF.

MDoF are selected at nodes where the mass is concentrated, force is applied, out-of-plane stiffness etc.

R-R method given in Anil K Chopra's book deals with transformation of displacement into Ritz shape vectors. This transformation converts the equation of motion (2nd order ODEs) into Ritz generalised co-ordinates. Up to here the procedure looks like Mode superposition method. Once it is transformed, selection of Ritz vector is carried out.

Regards,

- RD

## RR-RIiz approach

IS Ritz approach used in any commercial software? If yes, which one?

## Not in ANSYS

Ritz approach is not available in ANSYS.

- RD

## Guyan reduction

Thanks a lot, though you have mentioned a brief on Guyan reduction- is the concept of Guyan reduction from Ritz/Rayleigh Ritz? Can you mention a suitable reference for reading about Guyan reduction?

## Rober Cook.

No.

You may refere Rober Cook.

- RD